International Journal of Applied Science and Technology
Vol. 4, No. 6; November 2014
Detecting Variability and Trends in Daily Rainfall Characteristics in Amman-Zarqa
Basin, Jordan
Zain Al-Houri
Department of Civil Engineering
Applied Science University
Amman 11931
Jordan
Abstract
Rainfall has a great spatial and temporal variability. This variability has been manifested in many regions by
climate change phenomenon. In this paper, variability and trends in daily rainfall in Amman-Zarqa Basin in
Jordan have been detected. A number of parameters have been tested namely; number of rainy days, duration of
the wet season, maximum and average daily rainfall. The rainfall data sets consist of 15 rain gauge stations
located in the basin. Trends detection is carried out using time series plots, and Mann-Kendall test. The analyses
showed trend towards decreased duration of the wet season associated with decreased number of rainy days for
most of the stations. Furthermore, there is an increasing trend in the maximum and average daily rainfall for
most of the stations. However, results of Mann-Kendall test revealed that none of the parameters under study
showed statistically significant trends.
Keywords: Amman-Zarqa basin, climate change, daily rainfall, Mann-Kendall tau coefficient, trend analysis,
rainfall variability
1. Introduction
Variability in rainfall characteristics (type, amount, frequency, intensity and duration) is among the important
climate change impacts. Rainfall variability affects water resources sustainability which includes the availability,
management, and utilization of water resources. This in turn may affect ecosystems, land productivity,
agriculture, food security, water quantity and quality, and human health (EPA, 2014). Therefore, detailed
knowledge and analysis of rainfall regimes on different time scales are important prerequisites for enhancing the
management of water, planning and designing of hydraulic structures to mitigate the negative effects of floods
and droughts.
Many studies all over the world have been conducted to detect changing pattern and amounts of precipitation in
the last decades. Mansell (1997) investigated the effect of climate change on rainfall trends and flooding risks in
the west of Scotland. His study indicated that there is a significant increase in winter rainfall over the past 30
years.In addition, global climate predictions indicated that these trends are likely to continue for several decades
with obvious implications for flooding risk as well as water supply.Brunetti et al. (2001) analyzed seasonal and
annual precipitation and number of rainy days in northeastern Italy. Their results showed a negative trend in the
number of wet days associated with an increase in the contribution of heavy rainfall events to total precipitation.
Cook and Heerdegen (2001) studied rainy season in Australia and found out that the duration of the rainy and wet
seasons in northern Australia decreases with increasing latitude. Their study also indicated that the timing and
duration of these seasons were affected by the El Nino–Southern Oscillation (ENSO). Hsu (2004) conducted a test
and analysis for change existence in rainfall data using different statistical methods. His analysis yielded
consistent test results for most rainfall characteristics and geographic regions. Salami et al. (2010) carried out
statistical and trend analysis on a number of hydro-meteorological variables obtained from Jebba Hydropower
station including rainfall. In their analysis, rainfall was observed to have insignificant negative trend. Karmeshu
(2012) studied trends in annual precipitation for nine states in the Northeastern United States using Mann-Kendall
test. The Mann Kendall test demonstrated that there is an increasing trend in precipitation in only six states.
Almazroui et al. (2012) studied the seasonal climatology of the Arabian Peninsula for the period 1979–2009.
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In their study, they found out that, irrespective of season, rainfall insignificantly increased in the first period
(1979–1993), and then significantly decreased in the second period (1994–2009). Arun et al. (2012) studied the
changing trend of rainfall of a river basin of Orissa near the coastal region and observed overall insignificant
changes in the area.
In Jordan, the variability of precipitation over the past years has been detected by many researches (Al-Ansari et
al., 1999, Bani-Domi, 2005, Smadi et al., 2006, Ghanem, 2010). In addition, several researches have included the
climate change phenomenon and evaluated its impact on rainfall variation in Jordan (Cohen and Stunhill, 1996,
Ragab and Prudhomme, 2002, Tarawneh and Kadioglu, 2008, Abandeh, 1999, Dahamsheh and Aksoy, 2007,
Freiwana and Kadioglu, 2008, Hamdi et al., 2009, MoEnv, 2012, Matouqa, et al., 2013). Al-Ansari et al. (1999)
analyzed the rainfall in the Badia region, and concluded that there was a general decrease in rainfall intensity.
Tarawneh and Kadioglu (2002) conducted an analysis on precipitation records of 17 stations distributed according
to climatic regions of Jordan. Their analysis showed the high variability of rainfall of the country. Bani-Domi
(2005) conducted a trend analysis of seasonal and annual precipitation records in Jordan. His investigation
concluded that none of the precipitation series showed significant trends; however, the slope estimates showed
negative rates of change in the total annual rainfall for most stations. Smadi and Zghoul (2006) examined recent
changes, trends, and fluctuations in the total rainfall and number of rainy days at three stations in Jordan. Their
analysis showed a decline in the total rainfall and number of rain days in the second half of the past century.
Freiwan and Kadioglu (2008) examined different meteorological factors including annual, seasonal, and monthly
precipitation. Their results revealed insignificant, decreasing trend in precipitation. Hamdi et al. (2009) analyzed
data from six meteorological stations distributed around the country using several parametric and nonparametric
statistical approaches. Their results indicated that there are no visible trends indicating an increase or decrease in
the annual precipitation. Ghanem (2010) analyzed data of the rainy season over a 50-year period for 11 stations
distributed over Amman area. His analysis showed a decreasing trend of -0.4mm/year but with no statistical
significance. Matouqa et al. (2013) studied the climate change implication on Jordan using GIS and artificial
neural network for weather forecasting. Their results showed that no change has occurred in the mean annual
rainfall in both northern and eastern part, while it has increased in the central region of Jordan.
However, although previous studies investigated precipitation trend in the country, these studies were
concentrated mostly on annual scale analysis of rainfall records. Precipitation variability on different time scales,
daily scale in particular, is important since annual values of precipitation may obscure short-period features in the
rainfall pattern which in themselves might have great significance (Leopold, 1951). The variability in daily
rainfall events of various sizes, the changes in rainfall frequency (represented by number of rainy days), and the
length of the wet season may have important effect on the availability of water and vegetation, as well as, changes
in total annual rainfall. On the other hand, in recent years the country experienced an increase in the unusual
rainfall events of intense rainfall in a single-day that caused flash floods and considerable damage to human lives,
houses, agricultural land, and infrastructure facilities in portion of the country. Hence it is of great significance to
study how climate change phenomenon impacted the variability in the size and timing of daily rainfall events.
This work aims at detecting the variability and trends in the characteristics of daily rainfall events in the
basinrepresented by average daily rainfall, maximum daily rainfall, number of rainy days, and duration of the wet
season in Amman Zarqa basin in Jordan.
2. Materials and Methods
2.1 Site and Data Description
Amman-Zarqa basin (AZB) is a vital basin in Jordan. It is located north-west of Jordan, and it is approximately
4710 km2, 468 km2 of which is in Syria. Within the AZB, is the most important aquifer which is Amman-Wadi
Sir aquifer system (WRPS, 2000). Furthermore, the basin adjoins five of the densely populated governorates in
Jordan including; Amman, Zarqa, Jarash, Balqa, and Marfaq (Al-Mashaqbeh et al., 2014). Hence about 60 % of
the country’s population is living in the basin (Al-Omari et al., 2013).
This study is based on daily rainfall data available for 15 rainfall gauge stations distributed within AZB as shown
in Figure 1. The data were compiled from databases that are maintained by Ministry of Water and Irrigation in
Jordan. The 15 stations were selected according to data accuracy, availability, and adequate temporal coverage.
The length of data records for these gauges ranges from 47-77 years. Table 1 lists the name of each selected
station, its ID, and its period of coverage.
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International Journal of Applied Science and Technology
Vol. 4, No. 6; November 2014
2.2 Data Analysis
In this study, the longest records of daily rainfall data corresponding to 15 selected stations located in AZB were
analyzed to determine whether there is evidence of specific trends in the characteristics of daily rainfall events in
the basin. Four parameters have been tested in this work namely; average daily rainfall, maximum daily rainfall,
number of rainy days, and duration of the wet season. The trend analysis is performed using time series plots and
Mann-Kendall test. The methods of analysis include MINITAB statistical software (2010) and Addinsoft’s
XLSTAT software (2014).
The first step in the analysis was to extract the required data from the raw daily records maintained by the
Ministry of Water and Irrigation. The duration of the wet season is defined, in this work, as the time in days
between the first and last rainfall events in any water year. The extracted parameters are then subjected to basic
statistical and trend analyses to determine their variability in the basin.
The basic statistical analysis performed on the parameters considered in this study involves determination of the
measures of central tendencies (mean and median), the measure of dispersion (standard deviation, SD), the
measure of degree of symmetry in the distribution (skewness, SK), and the degree to which any data set is peaked
(Kurtosis, KT).
The trend analysis is performed using time series plots and Mann-Kendall test. Time series plots are used to
evaluate the variability in the selected parameters over time. For this part of the analysis, MINITAB statistical
software is used to create the time series plots. Linear trend model has been selected to fit the time series plots for
all the parameters considered in this work.
The Mann-Kendall test is a non-parametric statistical test that is widely used for trend detection in different
applications (Paulin and Xiaogang, 2005). This test is often used to test for presence of an increasing or
decreasing trend in the considered time series (Mann, 19450, Kendall, 1975, Gilbert, 1987). In this test, the null
hypothesis Ho is tested against the alternative hypothesis H1 where:
Ho: There is no trend in the data
H1: There is a trend in the data
According to the test, the null hypothesis (Ho) is rejected in favor of the alternative hypothesis (H1) at certain
probability level (α).
The Mann-Kendall test is based on the calculation of Kendall's tau (τ) coefficient which measures the association
between two ordinal variables. In this part of the study, Addinsoft’s XLSTAT software is used to evaluate the
trend in the selected parameters. Kendall's tau (τ) ranges from -1.0 to 1.0. A positive value indicates that the
rankings of both variables increase together. A negative value, on the other hand, indicates that as the rank of one
variable increases, the other decreases. If the two variables are independent, then the Kendall’s tau is expected to
be approximately zero (Abdi, 2007, Nelsen, 2001).
The following section presents the results of the trend analyses using time series plots and Mann-Kendall test
3. Results
3.1 Basic Statistics
The results of the basic statistical analysis for the parameters considered in this work are presented in Tables 2-5.
As illustrated in Table 2, the mean of average daily rainfall in the basin ranges from 3.8 mm in station AL0059 to
15.4 mm in station AL0005. The mean maximum daily rainfall in the basin ranges from 17.36 mm in station
AL0059 to 76.22 mm in station AL0005 as presented in Table 3.
As for the mean number of rainy days, and duration of the wet season in the basin, Table 4 illustrates that the
number of rainy days ranges from about 26 days to 45 days. While, the duration of the wet season varies from 155
to 187 days (as shown in Table 5) distributed in general between the months of October and May of any water
year.
The results revealed that the distribution for all the selected parameters is either positively skewed (when SK > 0)
or negatively skewed (when SK < 0). On the other hand, the kurtosis values for the parameters indicated either a
sharper than normal peak (when KT is positive), or flatter than normal peak distribution (when KT is negative).
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3.2 Trend Analysis Using Time Series Plots
Time series plots demonstrate that there are no generalized trends in the parameters under study over the past
years as shown in Figures 2 through 5. For example, linear trend analyses of maximum daily rainfall from
throughout most of the stations (10 out of 15 stations) have shown a general increase in extreme daily rainfall
events over the past years (Figure 2).
As for the average daily rainfall, the analysis did not detect a clear increasing or decreasing trend in all the
stations as illustrated in Figure 3. In the contrary, some stations showed an obvious increasing trend (AL0002,
AL0004, AL0018, AL0022, AL0027, AL0035, AL0045 and AL0047), while some stations showed a slight
decreasing trend (AL005, AL0028, AL0048, and AL0059). The remaining stations showed no clear increasing or
decreasing trend (AL0017, AL0019, and AL0036).
Linear trend analysis predicts a decreasing trend in the number of rainy days over the past years in all the stations
except for station AL0048 (Figure 4). The decreasing trend was also detected in the duration of the wet season at
all the stations except for stations AL0005, AL0017, and AL0022 (Figure 5). The analysis revealed that
variability in rainfall patterns led to an increase in the duration of dry periods in the past years.
3.3 Mann-Kendall Test
Tables 6 and 7 presents the results of the Mann-Kendall test, and null hypothesis test at 95% confidence level
(α=0.05) on the selected parameters for the 15 stations considered in this work. As illustrated in Table 6, by
running Mann-Kendall test on number of rainy days for the 15 stations, the test results in accepting the null
hypothesis Ho for most of the stations except for stations; AL0004, AL0019, AL0035, AL0036, and AL0047.
Accepting Ho indicates that there is no trend in the time series, and the result is statistically insignificant. On the
other hand, the values of Kendall's tau (τ) were all negative except for stations; AL0022, AL0028, and AL0048
indicating that the number of rainy days decreases with time.
As for the duration of the wet season, results of Mann-Kendall test revealed that there is no trend in the series for
all the stations (accepting the null hypothesis, Ho) except for two stations (AL0059 and AL0035) as indicated in
Table 6. The values of Kendall's tau (τ) were all negative except for stations; AL0002, AL0005, AL0017,
AL0018, and AL0022 indicating that the duration of the wet season decreases over the past years.
On running the Mann-Kendall test on maximum daily rainfall, the test revealed that there is no trend in the
maximum daily rainfall series for most of the stations except for stations; AL002, AL0004, AL0005, AL0035,
and AL0047 as shown in Table 7. The Kendall’s Tau (τ) values, however, are positive for eight of the stations
implying that the maximum daily rainfall increases with time.
Finally, for average daily rainfall data series, Mann-Kendall test revealed that no trends are statistically significant
for most of the stations except for stations; AL002, AL0019, AL0027, AL0045, and AL0047. The Kendall’s Tau
(τ) values are positive for 10 stations in the basin, implying that the average daily rainfall increases in general
over the past years (Table 7).
According to the observed decrease in number of rainy days and duration of the wet season, a special plan should
be considered for water and agriculture management to overcome the severity of dry periods. On the other hand,
with the general increase in occurrence of extreme precipitation events over the past years, the vulnerability for
flood risks might be aggravated in the future and consequently resulted in problems in the water storage
structures, sewer systems, and ineffectiveness in the performance of the waste water treatment systems existed in
the basin. Hence, understanding rainfall variability and trends in this variability is necessary to help policymakers
in managing water effectively in the country.
4. Conclusion
Rainfall variability is an important feature of semi-arid climates, and climate change is likely to increase this
variability in many of these regions. In this paper, the variability in four parameters including; number of rainy
days, duration of the wet season, maximum daily rainfall, and average daily rainfall in Amman-Zarqa basin are
examined. Linear trend and Mann-Kendall test have been used in this paper to detect the variability and trends in
these parameters. The results showed gradients in rainfall and rainfall variability across the basin. However there
was no conformity in the results obtained from the two tests.
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International Journal of Applied Science and Technology
Vol. 4, No. 6; November 2014
The trend lines in general identify a trend towards decreased number of rainy days throughout the basin, which is
associated with decrease in the duration of the wet season. Mann-Kendall test, on the other hand, demonstrated
that none of the parameters under study showed a generalized trend in all the station (at 5% significance level).
The paper discusses the continuous need for detecting rainfall variability, and trends in this variability to help
policymakers in managing water effectively in Amman-Zarqa basin. Continuous timely measures can certainly
help in conducting such studies and serve in accurately identifying the impact, if any, of climate change
phenomenon.
Acknowledgments
The author is grateful to the Applied Science University, Amman, Jordan, for the financial support granted to
cover the publication fee of this research article. The author is also thankful to Osama Saleh from the civil
engineering department at ASU for his aid in extracting the required data from the raw records obtained from
MWI.
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Figure1: Location of Amman-Zarqa basin in Jordan, and the Distribution of the Selected Rain Gauge
Stations within the Basin
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Vol. 4, No. 6; November 2014
Figure 2: Time Series Plots and Trend Detection for Maximum Daily Rainfall in AZB
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Figure 3: Time Series Plots and Trend Detection for Average Daily Rainfall in AZB
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International Journal of Applied Science and Technology
Vol. 4, No. 6; November 2014
Figure 4: Time Series Plots and Trend Detection in Number of Rainy Days in AZB
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Figure 5: Time Series Plots and Trend Detection in Duration of the Wet Season in Selected Stations in AZB
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Vol. 4, No. 6; November 2014
Table 1: Names, ID’s and Data Availability for the Selected Rain Stations in AZB
Station ID
AL0002
AL0004
AL0005
AL0017
AL0018
AL0019
AL0022
AL0027
AL0028
AL0035
AL0036
AL0045
AL0047
AL0048
AL0059
Station Name
Midwar
Jarash
Kitta
Sweilih
Jubeiha
Amman Airport
Amman Hussein College
Subihi
Rumeimin
K.H. nursery Evaporation Station (Baq'a)
Prince Feisal Nursery
Um Jauza
Sihan
Khaldiya
Um el Jumal Evaporation Station
Period of Record
1950-2013
1942-2013
1937-2013
1942-2013
1937-2013
1937-2013
1950-2013
1962-2013
1962-2013
1963-2013
1963-2013
1967-2013
1967-2013
1967-2013
1967-2013
Table 2: Summary Basic Statistics for Average Daily Rainfall (Mm) in AZB
Station ID Mean
(mm)
AL0004
9.2
AL0005
15.4
AL0017
12.0
AL0018
11.6
AL0019
5.8
AL0022
9.9
AL0027
12.2
AL0028
11.1
AL0035
8.7
AL0036
9.5
AL0045
14.1
AL0047
11.0
AL0048
4.8
AL0059
3.8
Median
(mm)
8.9
15.6
11.8
11.0
5.6
9.5
11.7
10.6
8.7
9.1
14.0
10.9
4.6
3.6
Max
(mm)
17.0
22.0
22.6
19.6
9.8
17.3
23.9
18.3
17.5
17.1
26.4
21.7
10.5
8.5
SD
SK
KT
2.4
3.8
4.5
3.1
1.4
2.5
3.8
3.1
2.8
2.6
4.3
3.2
2.1
1.2
1.0
-0.6
-0.4
0.2
0.8
1.1
1.0
0.3
0.3
1.0
0.3
1.4
0.3
1.3
1.4
0.7
1.6
2.4
0.4
1.4
1.0
-0.1
2.5
0.7
1.0
3.1
0.7
4.1
Number of
Elements
72
77
72
77
77
64
52
52
51
51
47
47
47
47
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Table 3: Summary Basic Statistics for the Maximum Daily Rainfall (mm) in AZB
Station ID
AL0002
AL0004
AL0005
AL0017
AL0018
AL0019
AL0022
AL0027
AL0028
AL0035
AL0036
AL0045
AL0047
AL0048
AL0059
Mean
(mm)
38.0
51.4
76.2
68.1
67.4
40.4
61.5
66.8
61.6
48.0
46.3
75.1
58.4
22.0
17.4
Median
(mm)
35.0
47.0
71.0
65.1
65.4
37.2
52.0
57.0
60.0
43.2
42.2
68.2
51.0
19.8
15.0
Max
(mm)
130.0
127.0
140.0
159.7
155.0
87.0
143.5
194.0
126.0
106.6
95.0
180.0
152.0
71.5
50.0
SD
SK
KT
21.5
18.7
26.4
31.6
27.1
16.5
25.5
33.7
22.5
19.6
15.6
34.7
27.7
11.7
8.9
1.8
1.2
0.4
0.2
0.8
1.3
1.4
1.8
0.8
0.8
0.9
1.3
1.8
1.8
1.4
5.0
2.9
-0.4
0.7
1.3
1.7
1.9
4.0
0.6
1.1
0.4
1.8
3.5
6.6
2.7
Number of
Elements
64
72
77
72
77
77
64
52
52
51
51
47
47
47
47
Table 4: Summary Basic Statistics for the Number of Rainy Days (Days) in AZB
Station ID
Mean
Median
Max
SD
SK
KT
AL0004
AL0005
AL0017
AL0018
AL0019
AL0022
AL0027
AL0028
AL0035
AL0036
AL0045
AL0047
AL0048
AL0059
39
35
38
41
45
38
34
33
38
35
34
36
26
30
39
34
38
40
45
37
33
32
39
35
34
33
25
28
59.0
59.0
67.0
70.0
79.0
64.0
54.0
60.0
60.0
52.0
56.0
55.0
47.0
51.0
10.0
10.0
11.7
11.1
12.3
9.5
11.2
9.7
11.5
9.1
9.4
10.5
9.7
9.4
-0.2
0.2
0.2
0.2
0.5
0.3
0.1
0.7
0.1
-0.4
0.1
0.1
0.5
0.3
0.0
-0.1
0.2
0.6
0.0
0.4
-0.5
1.1
-0.9
0.7
-0.3
-0.6
-0.6
0.3
22
Number of
Elements
72
77
72
77
77
64
52
52
51
51
47
47
47
47
International Journal of Applied Science and Technology
Vol. 4, No. 6; November 2014
Table 5: Summary Statistics for the Duration of the Wet Season (Days) in AZB
Station ID
AL0002
AL0004
AL0005
AL0017
AL0018
AL0019
AL0022
AL0027
AL0028
AL0035
AL0036
AL0045
AL0047
AL0048
AL0059
Mean
(Days)
155
177
171
178
180
187
178
169
172
177
181
168
174
164
173
Median
(Days)
160
182
174
175
179
188
174
169
169
176
178
168
171
168
174
Max
(Days)
220
230
215
243
383
229
390
341
383
242
357
209
350
224
230
SD
SK
KT
40.6
25.6
26.2
30.6
33.9
24.1
43.6
44.2
41.6
30.5
43.0
26.0
37.6
33.0
33.1
-1.5
-0.3
-0.4
0.1
2.8
-0.6
2.8
0.0
2.3
-0.7
2.2
-0.3
2.0
-1.0
-1.0
3.6
-0.3
-0.8
-0.1
16.0
0.3
12.0
7.2
12.3
1.2
8.2
-0.6
9.9
1.5
1.2
Number of
Elements
64
72
77
72
77
77
64
52
52
51
51
47
47
47
47
Table 6: Results of Mann-Kendall test for number of rainy days, and duration of the wet season in AZB
Station ID
AL0002
AL0004
AL0005
AL0017
AL0018
AL0019
AL0022
AL0027
AL0028
AL0035
AL0036
AL0045
AL0047
AL0048
AL0059
Number of Rainy Days
Kendall’s -τ
p-value
-0.018
0.839
-0.187
0.022
-0.034
0.669
-0.133
0.103
-0.121
0.126
-0.231
0.003
0.020
0.821
-0.117
0.229
0.007
0.950
-0.274
0.005
-0.225
0.022
-0.098
0.339
-0.367
0.0003
0.157
0.125
-0.111
0.283
Test Result
Accept Ho
Reject Ho
Accept Ho
Accept Ho
Accept Ho
Reject Ho
Accept Ho
Accept Ho
Accept Ho
Reject Ho
Reject Ho
Accept Ho
Reject Ho
Accept Ho
Accept Ho
Duration of the Wet Season
Kendall’s -τ
p-value
0.014
0.871
-0.088
0.278
0.084
0.287
0.154
0.058
0.044
0.579
-0.106
0.178
0.070
0.417
-0.119
0.218
-0.067
0.492
-0.232
0.017
-0.147
0.131
-0.111
0.279
-0.160
0.117
-0.133
0.193
-0.265
0.009
Test Result
Accept Ho
Accept Ho
Accept Ho
Accept Ho
Accept Ho
Accept Ho
Accept Ho
Accept Ho
Accept Ho
Reject Ho
Accept Ho
Accept Ho
Accept Ho
Accept Ho
Reject Ho
Table 7: Results of Mann-Kendall Test for Average and Maximum Daily Rainfall in AZB
Station ID
AL0002
AL0004
AL0005
AL0017
AL0018
AL0019
AL0022
AL0027
AL0028
AL0035
AL0036
AL0045
AL0047
AL0048
AL0059
Average Daily Rainfall
Kendall’s -τ
p-value
0.24
0.005
0.239
0.003
-0.184
0.018
-0.100
0.215
0.132
0.090
-0.001
0.996
0.101
0.242
0.113
0.243
-0.086
0.372
0.292
0.003
-0.009
0.935
0.149
0.143
0.388
< 0.0001
-0.089
0.384
-0.106
0.298
Test Result
Reject Ho
Reject Ho
Reject Ho
Accept Ho
Accept Ho
Accept Ho
Accept Ho
Accept Ho
Accept Ho
Reject Ho
Accept Ho
Accept Ho
Reject Ho
Accept Ho
Accept Ho
Maximum Daily Rainfall
Kendall’s -τ
p-value
0.192
0.026
0.116
0.154
-0.066
0.398
-0.049
0.547
0.101
0.196
-0.166
0.034
0.110
0.200
0.226
0.019
0.126
0.193
0.091
0.350
-0.061
0.537
0.239
0.018
0.253
0.013
0.092
0.369
-0.185
0.069
Test Result
Reject Ho
Accept Ho
Accept Ho
Accept Ho
Accept Ho
Reject Ho
Accept Ho
Reject Ho
Accept Ho
Accept Ho
Accept Ho
Reject Ho
Reject Ho
Accept Ho
Accept Ho
23